Question

Which of the following z-values, standard deviations, and sample sizes produce a margin of error of 0.95? m e = startfraction z times s over startroot n endroot endfraction z = 2.14; s = 4; n = 9 z = 2.14; s = 4; n = 81 z = 2.14; s = 16; n = 9 z = 2.14; s = 16; n = 81

Answer 1

The z-values, standard deviations, and sample sizes that produce a margin of error of 0.95 is  z = 2.14;  s = 4;  n = 81.

What is the margin of error?

The margin of error is a statistic that expresses how much random sampling error there is in a survey's results. The wider the margin of error, the less confident one should be that a poll result reflects the outcome of a population-wide survey.

The formula of the margin of error is given by the formula,

$MOE = Z_{\gamma}\times \dfrac{\sigma}{\sqrt{n}}$

A.)  z = 2.14;  s = 4;  n = 9

The margin of error is,

$MOE = Z_{\gamma}\times \dfrac{\sigma}{\sqrt{n}}$

$MOE = 2.14\times \dfrac{4}{\sqrt{9}}\\\\\\MOE =2.85$

B.) z = 2.14;  s = 4;  n = 81

The margin of error is,

$MOE = Z_{\gamma}\times \dfrac{\sigma}{\sqrt{n}}$

$MOE = 2.14\times \dfrac{4}{\sqrt{81}}\\\\\\MOE =0.9511$

C.)  z = 2.14;  s = 16;  n = 9

The margin of error is,

$MOE = Z_{\gamma}\times \dfrac{\sigma}{\sqrt{n}}$

$MOE = 2.14\times \dfrac{16}{\sqrt{9}}\\\\\\MOE =11.413$

D.)  z = 2.14;  s = 16;  n = 81

The margin of error is,

$MOE = Z_{\gamma}\times \dfrac{\sigma}{\sqrt{n}}$

$MOE = 2.14\times \dfrac{16}{\sqrt{81}}\\\\\\MOE =3.80$

hence, the z-values, standard deviations, and sample sizes that produce a margin of error of 0.95 is  z = 2.14;  s = 4;  n = 81.

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